pdf 6.58M

pK I exp.
10
9
8
7
6
5
4
3
2
AFMoC con : Incorporating ligand
and receptor conformational
variability into tailor-made
scoring functions
Serineproteases
r 2 = 0.85
1
8
1 2 3 4 5 6 7 8 9 10
Holger Gohlke
DrugScore
Frequency
Property
W = -ln[P]
„Potential“
Property
Gohlke, Hendlich, Klebe, JMB 2000.
Predicting binding affinities
pK i calc.
pK i exp.
1adc
Ferrara, Gohlke et al., JMC 2004.
14
12
10
6
Metalloenzymes
r 2 = 0.74
4
14
2
2 4 6 8 10 12 12 14
pK i calc.
• Data sets from LPDB
• Scaling of DrugScore
pK i= c * DrugScore
pK i exp.
10
8
6
4
2
0
0 2 4 6 8 10 12 14
pK i calc.
1ebg
Mixed: r 2 = 0.34
Scoring protein-ligand interactions
Identify binding mode
DrugScore
Prioritize ligands
pK i (calc)
-ln(g(R) / g ref (R))
3
2
1
0
-1
-2
pK i (exp)
Distance-dependent
pair potentials
1 2 3 4 5 6
R [Å] O N
R O O R
R
R
O
O N
R
O O R
Only non-H atoms + Fast +
General applicable + Tolerant against (exp.) errors
Beware of mass dependence
Recalc. with data from
Wang, Lu, Wang,
JMC 2003.
Correlation with
mass of the ligands
R S = 0.56
Velec, Gohlke, Klebe, JMC 2005.
1

Overview
Adaptation of Fields for Molecular Comparison
∑
p∈P
AFMoC
and
Docking
ΔP
= ΔW
)
g , t
t,
Τ(
p)
( rg
, p
AFMoC
and
Conformational
Variability
Predicting ‘hot spots’
Gohlke, Hendlich, Klebe, PD3 2000.
Methods in rational drug design
Candidate
Docking
QSAR
structure-based
information
ligand-based
information
Binding
mode
Binding
affinity
Intrinsic geometrical
information
R
HO
3.45Å
R
2.55Å
O
1.22Å
R
∠(C.2-O.2-O.3) = 128°
Phospholipase
(1poc)
Ca
ISOSTAR
HIV-1 protease
(1hvr)
O.sp2
C.sp3
Tailoring DrugScore towards
one specific protein
O.sp2
O.sp3
C.ar
Goal: Improvement of predictive power for pK i values
Idea:
& &
pK 1
i
pK 2
i
pK i 3
pK i n
2

Approach
“Potential field” * Property = Interaction field
T t
Interaction fields ...
... contain protein information
... are atom-type specific
... are orthogonal
... are „free energy“-fields
AFMoC
Adaptation of Fields for Molecular
Comparison
T 1
Comp. 1,
pK i 1
Comp. n,
pK i n
⎛c1
, Τ ⎞ 1 ⎜ ⎟
⎜ M ⎟
1
1
1
1
⎛
⎞
⎜ ⎟
1
ΔW1,
Τ LΔWg
Τ LΔW
Τ LΔWg
Τ ⎜
cg
Τ ⎟ ⎛ ⎞
⎜
⎟
pK
1
, 1 1,
t
, t , 1
i ⎜ ⎟
⎜M
O
M ⎟ * ⎜ M ⎟ = ⎜ M ⎟
⎜
⎟ ⎜ ⎟
⎜ n
n
n
n ⎟
⎜ n ⎟
⎝
ΔW
Τ LΔWg
Τ LΔW
Τ LΔWg
Τ ⎠
⎜c
1,
1,
Τ ⎟ ⎝ pK
1
, 1 1,
t
, t
t
i ⎠
⎜ ⎟
⎜ M ⎟
⎜ ⎟
⎝
cg
, Τt
⎠
# Unknowns c i,Τj > # Equations
c i,Τj from Partial-Least-Squares analysis
Results of PLS analysis
• Grid width: 1 Å,
Half-width of Gaussian: 0.85 Å
• Fields for:
aliphat. C
aromat. C
hydroxyl-O
carbonyl-O
carboxyl-O
amide-N
mercapto-S
N 61
q 2
sPRESS
r 2
0.62
1.34
0.97
S 0.37
F 166
C om ponents 10
Gohlke, Klebe, JMC 2002.
Approach
Correlation of interaction fields with known pK i values
q 0,4
0,3
2
T t
T 1
Comp. 1,
pK i 1
Comp. n,
pK i n
• 61 Inhibitors for training
⎛c1
, Τ ⎞ 1 ⎜ ⎟
⎜ M ⎟
1
1
1
1
⎛
⎞
⎜ ⎟
1
ΔW1,
Τ LΔWg
Τ LΔW
Τ LΔWg
Τ ⎜
cg
Τ ⎟ ⎛ ⎞
⎜
⎟
pK
1
, 1 1,
t
, t , 1
i ⎜ ⎟
⎜M
O
M ⎟ * ⎜ M ⎟ = ⎜ M ⎟
⎜
⎟ ⎜ ⎟
⎜ n
n
n
n ⎟
⎜ n ⎟
⎝
ΔW
Τ LΔWg
Τ LΔW
Τ LΔWg
Τ ⎠
⎜c
1,
1,
Τ ⎟ ⎝ pK
1
, 1 1,
t
, t
t
i ⎠
⎜ ⎟
⎜ M ⎟
⎜ ⎟
⎝
cg
, Τt
⎠
# Unknowns c i,Τj > # Equations
c i,Τj from Partial-Least-Squares analysis
Thermolysin
• Superimpositioning inside the binding pocket of
thermolysin using crystal structure templates
0,9
0,8
0,7
0,6
0,5
0,2
0,1
Internal validation
Leave-Five-Out
Leave-One-Out
Leave-Five-Out
0,0
0 1 2 3 4 5
run
6 7 8 9 10
Randomly selected pK i’s
# of components
0,0
1 2 3 4 5 6 7 8 9 10
-0,1
-0,2
q -0,3 2
-0,4
-0,5
3

Predictive power by variation
between generality and specificity
• 15 Thermolysin inhibitors for test set
• same treatment as before (“hand-docking”)
r 2
0,8
0,6
0,4
0,2
Original
pair potentials
PLS-model
0,0 0,2 0,4 0,6 0,8 1,0
θ
Predictive power by variation
between generality and specificity
• Mix “general” and “specific” results
pK = ( 1−θ
) pK + θ pK
i
Paar
i
PLS
i
• How much additional
information?
100 times random
choice of
5, 15, 30, 45, 53
training compounds
⇒ PLS model
⇒ prediction
r 2
0,8
0,6
0,4
0,2
0,0 0,2 0,4 0,6 0,8 1,0
θ
61
61
53
45
30
15
5
Predictive power by variation
between generality and specificity
• Mix “general” and “specific” results
pK = ( 1−θ
) pK + θ pK
i
Paar
i
PLS
i
r 2
0,8
0,6
0,4
0,2
Overview
Original
pair potentials
PLS-model
0,0 0,2 0,4 0,6 0,8 1,0
θ
Adaptation of Fields for Molecular Comparison
AFMoC
and
Docking
AFMoC
and
Conformational
Variability
A tailor-made objective function A tailor-made objective function
AFMoC obj
61
4

Docking HIV-1 protease inhibitors
# Complexes
60
50
40
30
20
10
• 66 complexes from
the PDB
• 48 compounds for
training
q 2 of the model > 0.6
• Consensus docking:
target structure 1ajv
• Docking using
AutoDock
Radestock, Böhm, Gohlke, JMC 2005.
Binding mode predictions
0
0 1 2 3 4 5 6
rmsd [Å]
AFMoC
*
obj
DrugScore
AutoDock
improvement
14%
train and test
data perform
equally well
Exploring new interactions
DrugScore: 4.5 Å rmsd
Fields for aliphatic C (C.3)
AFMoC obj : 0.8 Å rmsd
Processing of the fields
1. Column filtering
2. Remove repulsion
3. Mixing
“standard” PLS
PLS with Shannon
entropy based filtering
Accentuate important regions
DrugScore: 2.2 Å rmsd
Fields for hydroxyl O (O.3)
AFMoC obj : 1.4 Å rmsd
Further benefits from AFMoC obj
• Implicit consideration of multiple solvation
schemes
“flap water” absent “flap water” present
5

Binding affinity predictions
… in a multistep approach using AFMoC
Method
AFMoC obj
DrugScore
AFMoC
r 2
0.27
0.13
0.38
Recipe:
1. AFMoC obj for binding mode detection
2. AFMoC on „good“ modes for affinity prediction
Motivation: Use AFMoC on
homology models
Structure q 2 rmsd [Å]
Exp. 0.57 -
HM1 0.61 1.48 (2.90)
HM2 0.42 1.10 (2.35)
HM3 0.39 1.44 (3.37)
Exp.
HM1 HM2 HM3
60 loop
Approach I: Extended X-Matrix
⇒ Multimode binding
Overview
Adaptation of Fields for Molecular Comparison
AFMoC
and
Docking
AFMoC
and
Conformational
Variability
Idea: Inclusion of receptor and
ligand flexibility
+ + +
Consensus-Model
Consensus Model
Approach I: Extended X-Matrix
• „Obvious“ treatment
→ „Weighted fields approach“
→ ln K i = Σ w j ln K ij
→ K i = Π K ij wj WRONG!
• Right treatment
→ „Multimode binding approach“
→ K i = Σ K ij
→ Requires iterative solution of QSAR equation
Lukacova & Balaz, JCICS 2003
6

Approach II: Variable-Selection
Combination of multiple models
Models HM 1+2 HM 1+3 HM 2+3 HM 1+2+3
w/o varselect.
q 2 0.59 0.45 0.42 0.57
w/ varselect.
q 2 0.61 0.56 0.43 0.60
r 2 (test set) 0.64 0.61 0.41 0.64
Preval. 1 2 1 3 2 3 1 2 3
(Exp.: q 2 = 0.57; r 2 = 0.65)
0.50 0.50 0.50 0.50 0.51 0.49 0.38 0.33 0.29
Overview
con
Breu, Silber, Gohlke, JCIM 2007.
Adaptation of Fields for Molecular Comparison
AFMoC
and
Docking
Where to from here?
AFMoC
and
Conformational
Variability
Validation: Thrombin inhibitors
Structurally diverse
ligand set
Graphical
interpretation
Aromatic carbon
Exp. 1 / 2 / 3
1 + 2 + 3
If the protein moves …
„… deform binding pocket region accordingly“
7

Potential fields as elastic bodies
Problem: Determine displacement components
under prescribed forces
Solution: Elasticity theory via
Navier‘s equation
2 v
v v
μ∇
u + ( μ + λ)
∇Div
u + F = 0
Limiting conformational space
HIV-1 Protease
re: 0.30 Å
apo: 3.86 Å
def: 0.91 Å
- apo
- deformed
Repulsive fields of aromatic carbon
Elastic, adaptive potential grids
Kazemi, Krüger, Sirockin, Gohlke, ChemMedChem 2009.
Mimicking sidechain movement
CAPK
re: 0.33 Å
apo: 3.05 Å
def: 0.75 Å
- apo
- deformed
Scope and limitations Summary
Attractive fields of aromatic carbon
PHE122
- apo
- holo
• AFMoC incorporates additional structural and
energetic information about already known
ligands
• Binding-mode predictions can be improved
using AFMoC obj
• Conformational variability can be considered
using AFMoC con
• Possibility to mix adapted and original fields
• Implicit consideration of multiple solvation
schemes
8

Acknowledgements
• Sebastian Radestock
• Benjamin Breu
• Markus Böhm (Pfizer)
• Hans Velec (Marburg)
• Katrin Silber
• Gerhard Klebe
• DFG
• HWP/FIAS/FIGSS/OSS
• Merck, Darmstadt
• Boehringer, Biberach
• Novartis, Basel
9